Scottish Journal of Political Economy, Vol. 52, No. 2, May 2005
r Scottish Economic Society 2005, Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK
and 350 Main Street, Malden, MA 02148, USA
THE MISSING LINK BETWEEN
INFLATION UNCERTAINTY AND
INTEREST RATES
Hakan Berumentn, Zubeyir Kilinc and Umit Ozlalew
Abstract
In the literature, there is no consensus about the direction of the effects of inflation
uncertainty on interest rates. This paper states that such a result may stem from
differentiation in the sources of the uncertainties and analyzes the effects of
different types of inflation uncertainties on a set of interest rates for the UK within
an interest rate rule framework. Three types of inflation uncertainties – impulse
uncertainty, structural uncertainty and steady-state uncertainty – are derived by
using a time-varying parameter model with a Generalized Autoregressive
Conditional Heteroskedasticity specification. It is shown that the impulse
uncertainty is positively and the structural uncertainty is negatively correlated
with the interest rates. Moreover, these two uncertainties are important to explain
short-term interest rates for the period of inflation targeting era. However, this
time, the impulse uncertainty is negatively and the structural uncertainty is
positively correlated with the overnight interbank interest rates, which is consistent
with the general characteristic of the inflation targeting regimes. Lastly, the
evidence concerning the effect of the steady-state inflation uncertainty on interest
rates is not conclusive.
I
Introduction
There has been a keen interest on the part of both policymakers and
academicians in understanding the effects of inflation uncertainty on economic
performance. Considerable literature is devoted to the analysis of the effects of
inflation uncertainty on inflation, employment and output.1 Especially, after
price stability has emerged as the primary goal for monetary policy, it has often
been argued that a credible monetary policy is associated with lower inflation
uncertainty as mentioned in Clarida et al. (1999) and Johnson (2002).
Bilkent University
Author’s names appear in the alphabetical order.
1
For the effects of inflation uncertainty on inflation, Ball (1992), Ball and Cecchetti (1990),
Cukierman and Meltzer (1986), Cukierman and Wachtel (1979), Evans (1991), Evans and
Wachtel (1993) and Holland (1993 and 1995) find a positive relationship. For negative effects of
inflation uncertainty on employment, see Hafer (1986) and Holland (1986). Friedman (1977),
Froyen and Waud (1987) and Holland (1988) report a negative relationship between inflation
uncertainty and output.
n
w
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The literature regarding the relationship between inflation and interest rates
has intensified further in the last decade, especially after the emergence of price
stability as the overriding goal of monetary policy. Along with the dominance of
price stability, interest rates have become the main policy instrument during the
policymaking process. More importantly, this period witnessed the implementation of inflation targeting regimes in many industrialized economics, where
inflation uncertainty as well as inflation itself became more critical issues for the
policymakers. Surprisingly, despite the extensive literature concerning monetary
policy rules in an inflation targeting framework, there have been only a limited
number of studies, such as Johnson (2002) and Kontonikas (2004), which
analyze inflation uncertainty in an inflation targeting regime. While Johnson
(2002) studies four industrialized countries and finds that the decrease in
expected inflation during the inflation targeting period does not coincide with an
equal decrease in inflation uncertainty, Kontonikas (2004) reports that there has
been an improvement in inflation uncertainty for the UK during the inflation
targeting period.
In the transmission mechanism of inflation uncertainty on economic
performance, interest rates play a key role. Higher interest rates depress output
further by decreasing consumption and investment. More importantly, for many
emerging economies, where debt sustainability is still a critical issue, higher
interest rates deepen the debt burden and threaten the stability of the financial
system by leading to massive capital outflows, as stressed in Blanchard (2003).
On the other hand, finance theory suggests that risk is priced. Therefore, there
should be a positive relationship between inflation risk and return. Other
specifications, such as the asset pricing and term structure of interest rate
models, also suggest a positive relationship between inflation risk and interest
rates. Berument (1999), Chan (1994), Kandel et al. (1996), Fama (1975), Fama
and Gibbons (1982), Fama and Schwert (1977) and Mishkin (1981) provide
empirical evidence for this by using different specifications.
Although various studies find a positive relationship between interest rates
and inflation uncertainty, there are some important expectations. Hahn (1970)
reports a negative relationship between inflation uncertainty and interest rates
by employing the loanable funds theory. Furthermore, Juster and Wachtel
(1972a, b) and Juster and Taylor (1975) provide a negative relationship by
claiming that consumers seek to protect themselves against inflation and if the
variability of money income does not match inflation volatility, then the latter
will effect the real income variability because of loss of consumer confidence.
Thus, consumers will increase their savings, and this will cause consumption and
interest rates to decrease. Cukierman and Meltzer (1986), on the other hand,
argue that unanticipated inflation can be generated by governments in order to
stimulate their economies by decreasing interest rates.
Another line of literature, initiated by the theoretical works of Fischer (1975),
Merton (1975) and Malliaris and Malliaris (1991), argues that there is a positive
relationship between inflation uncertainty and real interest rates. When the
inflation rate is stochastic, the nominal interest rate is equal to the real interest
rate plus the sum of the expected inflation rate plus the covariance between the
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nominal rate and the inflation rate minus the variance of the rate of inflation.
Their specification suggests that there is a negative relationship between inflation
uncertainty and nominal interest rates.
After elaborating on the literature devoted to the effects of inflation
uncertainty on interest rates, it can be claimed that the overall impact is not
known a priori. The reason for this differentiation in the literature may stem
from the identification of different types of inflation uncertainties. Evans (1991)
defines three types of uncertainties and claims that their effects on the inflation
rate are different. Following his lead, we define three types of inflation
uncertainty: (1) the impulse uncertainty that is measured by the conditional
variance of inflation to capture the inflation risk, which could be induced for the
future by the information content of past inflation;2 (2) the structural
uncertainty, which captures the instability on the predictive power of past
inflation for the future; and (3) the steady-state uncertainty, which captures the
instability in the long run steady-state inflation rate.
In particular, we identify these three types of inflation uncertainties within a
time-varying parameter model with a Generalized Autoregressive Conditional
Heteroskedasticity (GARCH) specification. Next, in order to assess the effects
of these uncertainties on interest rates, we regress these three uncertainty
variables along with the expected inflation and output gap on a set of interest
rates for the UK. Then, we analyze their role in the monetary policymaking
process. The results are promising both from the perspective of the inflation
targeting and the role of inflation uncertainty in the policymaking process. The
empirical evidence provided in this paper suggests that there is a positive
relationship between impulse uncertainty and interest rates, and that there is a
negative relationship between structural inflation uncertainty and interest rates
for the period between 1962:06 and 2002:01. The evidence on the negative
relationship between steady-state inflation uncertainty and interest rates is weak.
However, once the era of inflation targeting is considered, then we could find a
statistically significant negative relationship between the overnight interbank
interest rates and impulse uncertainty.3 On the other hand, the relationship with
structural inflation uncertainty turns out to be positive.
The next section introduces the model, the data set and the motivation behind
the model selection. The third section reports the empirical evidence for the
model estimates, their interpretation and implications from a monetary policy
perspective. The final section concludes the paper.
II
The Model
Interest rate equation
The original Fisher equation is specified as the relationship between interest
rates and expected inflation. However, especially for overnight interest rates,
2
Such an uncertainty can also be seen to arise from the unforeseen shocks that hit the
economy.
3
The level of significance is at the 10% unless otherwise mentioned.
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which are viewed to be the main policy instruments for central banks, there are
other factors that they respond to. The first of these is the aggregate demand
pressure. It is well documented that output gap, which shows the pressure of
aggregate demand on price level, is a key variable in this context. Secondly,
interest rate smoothing could be another concept. As mentioned by Clarida et al.
(1999), central bankers avoid large changes in interest rates in short periods of
time. Instead, they adjust the interest rates slowly. Therefore, the original Fisher
equation can be modified with an interest rate rule such as
Rt ¼ a0 þ a1 petþ1 þ a2 gapt þ
p
X
a3;i Rti þ wt ;
ð1Þ
i¼1
where Rt is the nominal interest rate at time t, pet11 is the expected inflation for
time t11, gapt is the output gap at time t, wt is the residual term and p is the lag
order. The Fisher equation suggests that there is a positive relationship between
expected inflation and interest rates. Moreover, when actual output exceeds
potential level, the monetary authority will most likely increase interest rates
since the positive output gap, as a measure of excess aggregate demand, will put
extra pressure on inflation. When the output gap is negative, in order to
stimulate output, the Central Bank can follow in an accommodative way and
ease monetary policy.
In this paper, we consider another set of interest rates in addition to overnight rates. These interest rates vary in terms of liquidity, maturity, tax
treatment and their responsiveness to the market conditions. We also allow that
these interest rates are subject to changes in expected inflation and business cycle
conditions.
Modeling inflation uncertainty
One obvious method for measuring inflation uncertainty is the survey-based
approach as employed by Hafer (1986) and Davis and Kanogo (1996). Such an
approach measures uncertainty by the standard deviation of inflation forecasts.
Recently, Johnson (2002) employed absolute value of inflation forecast errors to
measure inflation uncertainty. However, Bomberger (1996) claims that using the
dispersion of the survey forecast does not provide a mean of measuring
uncertainty, rather it provides a way to measure disagreement. Furthermore, he
claims that some forecasters may try to avoid deviating from other’s forecasts,
which causes the value of expected inflation to be biased. Finally, Mankiw et al.
(2003) provides further support for the disagreement about survey results.
Another method would be to employ the Kalman Filter, which can be used
to measure the uncertainty regarding the structural variability of the parameters of an equation. In other words, this method is capable of measuring
inflation uncertainty by estimating the time-varying parameters of an inflation
specification.
Finally, one can use the Autoregressive Conditional Heteroskedasticity
(ARCH) or the GARCH processes, which measure the uncertainty concerning
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the inflation shocks by using the conditional variance of residuals.4 Grier and
Perry (1998) and Kontonikas (2004) are two recent examples adopting such a
methodology.
In this study, similar to Evans (1991), we combine the last two methods to
measure the three types of inflation uncertainty within a time-varying parameter
model with a GARCH specification. Formally, inflation uncertainty is modeled as:
ptþ1 ¼ Xt btþ1 þ etþ1 ;
ht ¼ h þ
m
X
fi e2ti þ
i¼0
btþ1 ¼ bt þ vtþ1 ;
where
n
X
etþ1 Nð0; ht Þ;
gi hti ;
ð2Þ
ð3Þ
i¼1
where vtþ1 Nð0; QÞ;
ð4Þ
where Xt is the set of explanatory variables for inflation, et is a normally
distributed error term with a time-varying conditional variance of ht and stands
for describing the shocks that hit the economy, bt11 is the parameter vector, which
is normally distributed with a homoskedastic covariance matrix of Q and vt11 is
the vector of shocks to bt11. Here, equation (3) is very important because it implies
that if past forecasts of inflation deviate substantially from the observed inflation,
uncertainty will increase.
In the model, the inflation equation is specified as a kth order time-varying
autoregressive process and the residuals of the inflation equation follow a
GARCH process. In such a setting, the Kalman Filter enters into the process for
two reasons. Firstly, in a time-varying parameter framework, the Kalman Filter
emerges as an efficient estimation method. Secondly, and more importantly, the
updating equations regarding the Kalman Filter enable us to decompose
different types of inflation uncertainties. These updating equations are:
ptþ1 ¼ Xt Et btþ1 þ Ztþ1 ;
ð5Þ
Ht ¼ Xt Otþ1jt XtT þ ht ;
ð6Þ
Etþ1 btþ2 ¼ Et btþ1 þ ½Otþ1jt XtT Ht1 Ztþ1 ;
ð7Þ
Otþ2jtþ1 ¼ ½I Otþ1jt XtT Ht1 Xt Otþ1jt þ Q:
ð8Þ
In the Kalman Filter updating equations, equation (6) clearly shows that two
types of ‘variability’, which cause two types of uncertainties, can be decomposed.
Equations (7) and (8) show how past forecast errors are built into new estimates
about inflation, which provides a link from inflation uncertainty to inflation.
The conditional covariance matrix of bt11, which represents the role of the
structural uncertainty in the inflation process, is denoted by Ot11|t. Equation (7)
shows the innovations in updating the estimates of bt11, which are used for
forecasting future inflation. The updating of the conditional distribution of bt11
4
The ARCH model was first introduced by Engle (1982) and the GARCH model is provided
by Bollerslev (1986).
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over time in response to new information is also shown in equations (7) and (8).
Thus, this model enables us to evaluate the uncertainties that originate from
both inflation shocks (et11) and the structure of the inflation (vt11).
In the model presented above, ‘e’ can be viewed as describing the shocks that
hit the economy. Then, the time-varying parameter b will show how these shocks
are propagated through the economy. Such terminology leads us to Frisch and
Slutsky’s distinction between impulses and propagation.5 As a result, we can
refer to inflation uncertainty associated with randomness in b as ‘structural
uncertainty’, which we measure by XtOt11|tXTt , while the uncertainty associated
with randomness in ‘e’ can be called ‘impulse uncertainty’, which is measured by
the conditional variance of et11(ht).
In addition to structural and impulse uncertainties, we employ the steadystate inflation uncertainty as the third type of inflation uncertainty measure. We
believe that this might capture the credibility of central banks in their long-term
commitment to control inflation. In particular, the inflation equation is defined
as an AR(2) process:6
ptþ1 ¼ b1; tþ1 þ b2; tþ2 pt þ b3; tþ3 pt1 þ etþ1 :
ð9Þ
Therefore, the steady-state inflation is defined as
ptþ1 ¼ ð1 b2; tþ1 b3; tþ1 Þ1 b1; tþ1
ð10Þ
and the conditional variance of steady-state inflation is
H2t ðptþ1 Þ ¼ HEt btþ1 Otþ1 HEt b0tþ1 ;
ð11Þ
where
2
3
½1 Et b2; tþ1 Et b3; tþ1 1
6
7
HðEt btþ1 Þ0 ¼ 4 Et b1; tþ1 ½1 Et b2; tþ1 Et b3; tþ1 2 5:
2
Et b1; tþ1 ½1 Et b2; tþ1 Et b3; tþ1 ð12Þ
Finally, after defining the three sources of inflation uncertainty, we can
modify the interest rate specification (equation (1)). The positive relationship
between interest rate and inflation uncertainty, as suggested by Berument (1999),
Chan (1994), Fama (1975), Fama and Gibbons (1982), Fama and Schwert
(1977) and Mishkin (1981), can be elaborated further now. In particular, we
extended Berument (1999) by allowing the output gap to enter the interest rate
specification and using three different types of inflation uncertainty. Thus, we
estimate the following specification:7
5
For a detailed discussion, see Blanchard and Fischer (1989, p. 277).
Following Engle (1982), we also estimated a version of the Phillips curve, which also
includes real wages in the inflation specification. However, in those specifications, the real wage
variable could not explain the behavior of prices in a statistically significant fashion. This
finding is parallel to Berument (1999). Therefore, in order to avoid over-parameterization, we
drop the real wage variable from the inflation specification and model the inflation as an AR
process.
7
We plot the impulse, structural and steady-state uncertainty of inflation variables in Figures
1–3, then briefly discuss these plots in the Appendix.
6
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2.00
1.75
1.50
1.25
1.00
0.75
0.50
0.25
1961 1965 1969 1973 1977 1981 1985 1989 1993 1997 2001
Figure 1. Impulse inflation uncertainty.
Rt ¼ a0 þ a1 petþ1 þ a2 gapt þ
p
X
i¼1
þ
a6 H2t ðptþ1 Þ
a3; i Rti þ a4 ht þ a5 St
ð13Þ
þ wt ;
where St is the structural uncertainty, which denotes XtOt11|tXTt . ht and H2t ðptþ1 Þ
stand for the impulse uncertainty and steady-state uncertainty, respectively.
Furthermore, pet11 is the forecast value of inflation (from equation (9)), gapt is
the deviation of output from its long-run trend, which is calculated with the HP
filter. In addition, a0 is the constant term, a1 is the coefficient for the expected
inflation, a2 is the coefficient for the output gap, a3,i is the coefficient of the ith
lagged value of the interest rate, a4 is the coefficient for the impulse uncertainty,
a5 is the coefficient for the structural uncertainty and a6 is the coefficient for the
steady-state uncertainty. Equation (13) can also be regarded as ‘Enriched
Taylor-Type’ rule, where there is room for adding the inflation uncertainty,
other than the response of interest rate to price stability and output stability
together with its lagged values.
Instead of estimating the inflation specification and interest rate equations
jointly, we estimate the inflation equation with the rolling regression method by
using all the sample data that is known at a given time for the estimation of the
parameters. If we estimated the inflation and the interest rate specifications
jointly, then we would be implicitly assuming that agents know the inflation
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1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1961
1965
1969
1973
1977
1981
1985
1989
1993
1997
2001
Figure 2. Structural inflation uncertainty.
rates for the full sample to estimate bt11 for each t11. In particular, by using
rolling regressions; first, we estimate equations (5)–(8) and (11) for each t. Then
we use these estimates to calculate the expected inflation and three uncertainty
measures for time (t11)th observation. Finally, we include these derived series in
the interest rate specification.
Data Set
We use monthly UK data from 1961:06 to 2002:2. The main reason for choosing
the UK to assess the effects of different types of inflation uncertainty on interest
rates is the vast amount of literature devoted to inflation uncertainty for the UK,
pioneered by Engle (1982). The inflation series is obtained by taking the
logarithmic first difference of the seasonally adjusted CPI series. For robustness
purposes, we consider several types of interest rates, which vary in terms of
liquidity, maturity, tax treatment and their responsiveness to market conditions:
the Overnight minimum interbank interest rate, the Treasury bill rate, the
Treasury bill rate bond equivalent, the Deposit rate, the Lending rate (clearing
banks) and the Government bond yields (both short- and long-term). It is
important to note that all of these series are not available for the full sample size:
the data for the Overnight interbank interest rate is available after 1972:01; the
Treasury bill rate data is available after 1964:01; Treasury bill rate bond
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3.0
2.5
2.0
1.5
1.0
0.5
0.0
1961
1965
1969
1973
1977
1981
1985
1989
1993
1997
2001
Figure 3. Steady-state inflation uncertainty.
equivalent data is available after 1974:06; the Deposit rate data is available after
1961:01; the Lending rate data is available after 1966:06; Government bond
yields (short-term) data is available after 1966:01; and Government bond yields
(long-term) data is available after 1961:06.
An important remark about the estimation process is that while estimating
the inflation, we did not include the conditional variance to the inflation
specification. There is considerable literature regarding the positive relationship
between inflation and inflation uncertainty. However, the direction of this
relationship is a subject of debate. Following, Grier and Perry (1998), we did not
include inflation uncertainty in the inflation specification.8 We also included two
intercept dummy variables, which characterize the institutional developments
that the Bank of England pursued during the sample period. These dummies
stand for the adoption of an inflation targeting regime for the post October 1992
era and the change in the independence of the Bank of England for the post May
1997 era. Several studies including Johnson (2002), Kontonikas (2004) and
8
The positive relationship between inflation and inflation uncertainty is often elaborated in
the literature. However, the direction of the effect is still an unsettled issue: whether inflation
uncertainty causes inflation or inflation causes inflation uncertainty. Grier and Perry (1998)
argue that for the UK inflation causes inflation uncertainty, the evidence for the reverse is weak.
This is similar to our experiments – not reported in the text. Thus, we did not include the
inflation risk in the inflation specification.
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Nelson (2000) report that the nature of monetary policy changed significantly
after the implementation of inflation targeting. Communicating more clearly the
goals of monetary policy and creating accountability for the achievement of
goals led to a decline in expected inflation. Granting more independence to Bank
of England further strengthened the positive aspects of the inflation targeting
framework. Therefore, two dummies about these two institutional features are
included in the regressor matrix.
Justification of the Model
The purpose of this sub-section is to justify the selection of the GARCH–
Kalman Filter specification that is used in this paper. Parallel to Berument
(1999) and Grier and Perry (2000), we model the inflation equation as an AR
process which is enriched with two types of level dummies. The lag order is
selected by the Final Prediction Error Criteria (FPE), which selects the optimal
lag length such that residuals of the inflation equation are no longer
autocorrelated. This is important because ARCH-LM tests of autocorrelated
residuals wrongly suggest the presence of an ARCH effect, even when there is no
ARCH effect (see, Jansen and Cosimona (1988)). The FPE criteria suggests the
lag order of two. Next, we estimate the inflation equation as an AR(2) process
and apply the ARCH-LM test for the 1, 6 and 12 lags, respectively. The ARCHLM test statistics are 64.142, 79.617 and 85.544 for these three lags. These test
statistics clearly suggest the presence of an ARCH effect. Various specifications
of GARCH are considered next. GARCH(1,1) is selected as the process to assess
the conditional variance.
Time-varying parameter models give superior estimates to many other
estimation techniques since the time-varying parameter b will show how the
shocks hitting the inflation dynamics are propagated through the system over
time. Different specifications for the evolution of the parameters are also
estimated. These specifications include models with a return-to-normality
assumption, which can be written as:
¼ Fðb bÞ
þ vtþ1
ðbtþ1 bÞ
t
and models with constant mean, which take the form:
þ vtþ1 :
btþ1 ¼ F b
However, the evidence from Table 1 suggests that the random walk
assumption used in this study outperforms its alternatives, both in terms of
Schwarz Information Criteria and Akaike Information Criteria.
III
Empirical Evidence
Table 2 reports a set of unit root tests with a constant term for the inflation rate
and seven interest rates. The first three tests – Dickey-Fuller, Augmented
Dickey-Fuller and Phillips and Perron – take the presence of unit root as their
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Table 1
Model selection criteria
Our model
Model with return-To normality assumption
Model with constant mean
AIC
SIC
3.15
3.96
4.18
3.68
3.99
4.21
AIC, Akaike Information Criteria; SIC, Schwarz Information Criteria.
Table 2
Unit root tests
Inflation
Ovenight minimum interbank rate
Treasury bill rate
Treasury bill rate bond equivalent
Deposit rate
Lending rate (clearing banks)
Government bond yields (short-term)
Government bond yields (long-term)
DF
ADF
PP
KPSS
12.212n
3.067
1.836
1.196
2.106
1.594
1.710
1.016
4.570n
2.034
2.524
1.911
2.408
1.848
2.078
1.285
12.491n
2.446
2.379
1.788
2.407
1.781
2.133
1.268
1.761n
1.110n
1.418
3.103n
2.011n
1.500n
2.252n
2.160n
Note:
n
indicates rejecting the null at the 5% level.
DF, Dickey-Fuller; ADF, Augmented Dickey-Fuller; PP, Phillips and Perron; KPSS, Kwiatowski, Phillips,
Schmidt and Shin.
null hypothesis. Except for inflation, we cannot reject the null hypothesis for the
variables in interest. This is similar to Berument and Froyen (1998). However,
failing to reject the null hypothesis does not mean that one can accept the
alternative. Thus, we also report the Kwiatowski, Phillips, Schmidt and Shin test
in the last column and with this test, we can reject the null hypothesis of
stationarity for all of the variables. Therefore, we assume all the variables of
interest have unit roots.
Table 3 reports the parameter estimates of equation (1) when the expected
inflation is gathered from the predicted value of equation (9) for the whole
sample by using the OLS method. The estimated coefficients for the expected
inflation and the output gap are always positive, which is consistent with the
economic priors. These coefficients are statistically significant only when the
interest rate is taken as the overnight minimum interbank rate and the lending
rate. The last three columns report the estimated coefficients of lag dependent
variables up to three lags, where the lag order is determined by the FPE for the
largest lag length among seven interest rates. The positive coefficient for the
output gap suggests that interest rate increases when there is an inflation
pressure. Note that we include three lagged values of the dependent variables on
the right-hand side; therefore, we cannot interpret the coefficients of the
expected inflation to see the interest rates increase more or less than the expected
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0.034n (1.760)
0.007 (1.265)
0.006 (0.990)
0.008 (1.167)
0.010nn (2.515)
0.004 (0.721)
0.001 (0.348)
0.002 ( 0.133)
0.015nn (2.952)
0.014nn (2.392)
0.014nn (2.896)
0.013nn (2.471)
0.016nn (2.283)
0.005 (1.224)
0.074n (1.796)
0.020 (1.456)
0.019 (1.010)
0.036 (1.610)
0.035nn (2.163)
0.004 (0.335)
0.006 (0.646)
gapt
0.583nn
1.351nn
1.408nn
1.146nn
1.092nn
1.318nn
1.340nn
(5.599)
(17.421)
(17.851)
(18.181)
(18.372)
(20.526)
(22.978)
Rt 1
0.142 (1.453)
0.422nn ( 3.707)
0.513nn ( 4.375)
0.181nn ( 2.244)
0.149n ( 1.804)
0.413nn ( 4.563)
0.482nn ( 5.312)
Rt 2
0.247nn (2.561)
0.045 (0.807)
0.081 (1.340)
0.003 (0.073)
0.033 (0.555)
0.071 (1.412)
0.134nn (2.294)
Rt 3
Note:
t-statistics are reported in parentheses next to the corresponding coefficients where standard errors are calculated with the Newey–West’s heteroskedastic consistent formula.
n
Significance at the 5% level; nnSignificance at the 10% level.
Overnight minimum interbank rate
Treasury bill rate
Treasury bill rate bond equivalent
Deposit rate
Lending Rate (clearing banks)
Government Bond yields (short-term)
Government Bond yields (long-term)
pet11
Constant
Table 3
Estimates of the Fisher equation: 1961:06–2000:02
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inflation. In order to observe the long-run effect of inflation on interest rates,
one needs to estimate (1 a31 a32 a33) 1a1. If this coefficient is observed to
be greater than one, then this suggests that interest rates increase more than the
expected inflation. Alternatively, the estimated (1 a31 a32 a33) 1a1 being
less than one would suggest that interest rate increases are less than the expected
inflation. The estimates are always less than one for all of the interest rates
except the overnight minimum interbank interest rate (not reported here). This is
quite important, since the Bank of England can control the overnight minimum
interbank rate and affect the other types of interest rates. The Bank of England’s
increasing the short-term interest rate more than expected inflation indicates a
tight monetary policy. The estimate of (1 a31 a32 a33) 1a1 is 1.21, and this
suggests that as expected inflation increases by 1%, the Bank of England
increases the nominal interest rate by 1.21% or the expected real interest rate by
.21%.
Next, in order to evaluate whether the derived inflation uncertainty series
play any role in the interest rate rule for the monetary authority, three types of
uncertainties are added to the regression equation presented in Table 3. A brief
elaboration of these three inflation uncertainty measures are provided in the
Appendix. The estimates are reported in Table 4.9
The estimates of the coefficient for the impulse uncertainty, ht, are always
positive for all of the interest rates, and the estimated coefficients for the
structural uncertainty, St, are always negative, but these estimates are not
statistically significant for the overnight minimum interbank rate. The estimates
for the coefficients of impulse uncertainty are parallel with Berument (1999),
Chan (1994) and Fama (1975). Interest rates increase with higher impulse
uncertainty. The negative coefficients of the structural uncertainty are parallel
with Hahn (1970), Juster and Wachtel (1972a, b) and Juster and Taylor (1975).
The estimated coefficients for the expected inflation and output gap are always
positive, and these coefficients are statistically significant when the interest rate is
taken as the overnight interest rate and the lending rate. The positive coefficient
for the output gap parallels the economic priors mentioned in the ‘Interest Rate
Equation’. Lastly, the estimate of (1 a31 a32 a33) 1a1 is greater than one
only for the overnight interest rate, but it is not statistically significant. This
9
As a robustness test, we report the inflation and conditional variance specification for the
full sample (standard errors are reported in parentheses under the corresponding estimated
coefficients.) where D1t is the dummy variable for the post-October 1992 era and D2t is the
dummy variable for the pre-May 1997 era. Here, the estimates of the GARCH(1,1) specification
is of interest. Estimated coefficients of GARCH(1,1) specification are all positive and
statistically significant. This satisfies the non-negativity condition of the variance. Moreover,
the estimate of the sum of (f11g1) is less than one, which satisfies the non-explosiveness of the
estimated conditional variances. Thus, the robustness tests provide support for our
specification.
ptþ1 ¼ 0:4219 0:1636pt 0:2384pt1 0:274D1t þ 0:0702D2t þetþ1
ð29:83Þ
ð11:57Þ
ð23:84Þ
ht ¼ 0:028 þ 0:238e2t þ 0:632ht1
ð1:98Þ
ð3:51Þ
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ð5:68Þ
ð5:98Þ
ð1:88Þ
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0.016 (0.855)
0.006 (0.789)
Rt 1
0.015 ( 0.960) 0.594nn (6.009)
H2t (pnt11)
0.132 (1.378)
Rt 2
0.258nn (2.665)
Rt 3
0.075nn ( 2.285) 0.001 ( 0.264) 1.408nn (17.741) 0.509nn ( 4.367) 0.076 (1.280)
0.069nn ( 2.029) 0.001 ( 0.110) 1.351nn (17.323) 0.421nn ( 3.704) 0.043 (0.778)
0.024 ( 0.285)
St
0.005 (0.397)
0.004 (0.509)
0.002 (0.196)
0.003 (0.462)
0.001 (0.212)
1.301nn (20.988) 0.392nn ( 4.393) 0.063 (1.249)
0.025nn (3.447) 0.068nn ( 4.042) 0.002 ( 0.592) 1.327nn (22.774) 0.468nn ( 5.106) 0.136nn (2.324)
0.037nn (2.518) 0.090nn ( 2.823)
0.006 (0.702)
0.034 (1.522) 0.041n (1.663) 0.095n ( 1.894) 0.001 ( 0.100) 1.149nn (18.115) 0.182nn ( 2.248) 0.003 (0.067)
0.016nn (3.064) 0.029n (1.892) 0.049nn (2.250) 0.108nn ( 2.429) 0.007 ( 1.538) 1.106nn (18.166) 0.158n ( 1.866) 0.035 (0.574)
0.030n (1.911)
0.028n (1.719)
0.019 (1.373)
0.006 (0.925)
ht
0.067n (1.667) 0.022 (0.595)
gapt
0.055 (1.609)
pet11
Note:
t-statistics are reported in parentheses next to the corresponding coefficients where standard errors are calculated with the Newey–West’s heteroskedastic consistent formula.
n
Significance at the 5% level; nnSignificance at the 10% level.
Overnight
0.011 ( 0.552)
minimum
interbank rate
Treasury bill
0.011 (1.589)
rate
Treasury bill
0.012 (1.568)
rate bond
equivalent
Deposit rate
0.007 (0.850)
Lending rate
0.002 (0.211)
(clearing
banks)
Government
0.014 (1.535)
bond yields
(short-term)
Government
0.001 (0.108)
bond yields
(long-term)
Constant
Table 4
Estimates of the interest rate specification – Whole Sample (1961:06–2002:01)
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235
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H . B E RU M E N T , Z . KI L I N C A N D U . O Z L A L E
suggests that the interest rate increases more than expected inflation for
overnight rates in the long run, while other interest rates increase less than the
increase in inflation.
Inflation Targeting Period
In October 1992, The Bank of England adopted an inflation targeting regime.
This policy shift, which could induce structural changes in the macroeconomic
environment, could not be addressed simply by the dummy variable in equation
(2). Thus, we re-estimate the whole system for the post-inflation targeting
regime, for which the results are presented in Table 5. None of the estimated
coefficients for the impulse uncertainty and structural uncertainty are
statistically significant except the ones for the overnight minimum interbank
interest rates. The estimated coefficients for steady-state inflation uncertainty
have alternating signs across interest rates, but only for the deposit rate and
government bond yields (short-term) are these coefficients statistically significant. The estimates on the overnight interbank rate are important. Bearing in
mind that the overnight rate is the main policy instrument for the Bank of
England especially after the implementation of inflation targeting, the results
imply that the uncertainties related to the structure of the inflation process and
the long-run level of inflation induce the Bank of England to increase interest
rates, while any uncertainty because of unforeseen shocks leads the monetary
authority to ease its policy. The estimates on the overnight rate make sense in
terms of an inflation targeting framework. When the monetary authorities
announce their inflation targets, they make it explicit (in order to enhance
credibility), that any uncertainty that could lead to a permanent change in the
structure of the inflation or its long-run level will be eliminated. Therefore,
agents in the economy can have a clearer idea about the long-term goals of the
monetary authority. The finding that overnight interest rates, as the main policy
instrument of the Bank of England, drop because of an increase in impulse
uncertainty can be explained within the context of ‘escape clauses’, which are
inherent in an inflation-targeting framework. It should be once again mentioned
that impulse uncertainty stems mostly from unforeseen shocks that are viewed to
be temporary. If a shock is perceived to be temporally such that it does not affect
the long-term goals of central banks, then there is room for central banks to
change the short-term interest rates to accommodate temporary shocks. As
Bernanke et al. (1999, p. 24) states, those escape clauses even permit a central
bank to change its medium-term targets in response to unexpected developments, such as supply shocks that cause impulse uncertainty to increase. A
similar line of argument is also proposed by Clarida et al. (1999). They argue
that when central banks are faced with unforeseen shocks, then central banks are
allowed to implement accommodative monetary policy, so long as the structure
of the inflation path and the long-term inflation targets are not distorted.
Finally, the coefficients for the output gap in each equation are positive,
implying that the Bank of England increases interest rates to curb any demand
pressure that might be inflationary. However, the t-statistics for that coefficient
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pet11
gapt
ht
St
H2t (pnt11)
0.202 (1.546)
0.115 (1.077)
(15.281) 0.652nn ( 3.352)
(12.360) 0.339nn ( 2.212)
Note:
t-statistics are reported in parentheses next to the corresponding coefficients where standard errors are calculated with the Newey–West’s heteroskedastic consistent formula.
n
Significance at the 5% level; nnSignificance at the 10% level.
0.022 ( 0.105)
0.339nn ( 2.343)
(7.322) 0.297 ( 1.167)
(9.455)
0.117 (0.566)
0.110 (1.328)
Rt 3
0.080 (0.544)
0.145 (1.478)
0.375nn (2.964)
Rt 2
(17.422) 0.631nn ( 2.736)
(16.439) 0.649nn ( 3.998)
(2.264)
Rt 1
Overnight minimum 0.094nn (3.818) 0.060nn (2.292) 0.060n (1.745) 0.113nn ( 3.669) 0.222nn (3.368) 0.007 (0.414)
0.315nn
interbank rate
0.004 (0.197) 0.013 (0.842) 0.010 ( 0.756)
0.018 (0.624) 0.002 ( 0.388) 1.461nn
Treasury bill rate
0.043n (1.739)
Treasury bill rate
0.050n (1.714)
0.004 (0.153) 0.027 (1.339) 0.019 ( 1.028)
0.034 (0.902) 0.002 ( 0.233) 1.405nn
bond equivalent
0.010 (0.493)
0.009 ( 0.201) 0.030nn (2.546) 1.126nn
Deposit rate
0.048nn (3.162) 0.009 ( 0.580)0.076 (1.513)
0.003 (0.202)
0.005 ( 0.198) 0.001 (0.232)
1.150nn
Lending rate
0.036nn (2.182) 0.009 ( 0.569)0.022 (1.181)
(clearing banks)
Government bond 0.041nn (2.055) 0.011 ( 1.134)0.016 (0.902) 0.003 ( 0.181)
0.000 (0.008) 0.017n ( 1.668)1.389nn
yields (short-term)
Government bond 0.009 (0.813)
0.002 (0.249) 0.016 (1.086)
0.001 (0.051)
0.016 ( 0.450) 0.010 ( 1.342) 1.210nn
yields (long-term)
Constant
Table 5
Estimates of the interest rate specification for the Post Inflation Targeting Era (1992:10–2002:01)
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H . B E RU M E N T , Z . KI L I N C A N D U . O Z L A L E
are mostly low and the response of interest rates to the output gap is generally
lower than the response to expected inflation, which also implies that price
stability has become a more dominant factor in the monetary policy making
process after the adoption of inflation targeting.
IV Conclusion and Policy Implications
There are conflicting views about the effects of inflation uncertainty on interest
rates. While some studies find evidence of a positive effect of inflation
uncertainty on interest rates because of an increase in the inflation risk
premium, others argue that higher saving incentives under higher inflation
uncertainty or political motives to generate surprise inflation may actually lead
to a negative relationship between those two variables. However, most of these
studies stop short of breaking down inflation uncertainty to its components and
analyzing the effects of each type of uncertainty on the interest rates.
This paper analyzes the impact of different types of inflation uncertainties on
interest rates for the UK within the context of a time-varying parameter model
with GARCH specification. Since the relationship between inflation uncertainty
and interest rates may have changed significantly after the implementation of the
inflation targeting regime, the role of each type of inflation uncertainty in the
monetary policy reaction function is also investigated for the inflation targeting
period. It is shown that when the whole sample is considered, the impulse
uncertainty is positively, and the structural inflation uncertainty is negatively
correlated with interest rates.
When the inflation targeting period is considered alone, the results imply that
any uncertainty regarding the structure or the long-run level of the inflation
process causes the Bank of England to follow a tight monetary policy and
increase the overnight interest rates, which is the main policy instrument for that
particular period. On the other hand, if the uncertainty arises because of
unforeseen shocks, then monetary policy has an accommodative characteristic.
The results are also promising in terms of policy implications. In an inflation
targeting framework, where price stability incentives and long-term goals of
monetary policy are explicitly stated, two distinctive characteristics emerge:
credibility and accountability. An increase in inflation uncertainty that would
change either the structure of inflation dynamics or the long-run level of
inflation has the potential to disrupt these two features and undermine the
success of the regime. Taking this fact into consideration, the monetary
authorities seem to attempt to eliminate such uncertainties. On the other hand, if
the uncertainty emerges because of unforeseen shocks that are mostly viewed as
temporary, then monetary policy can be accommodative and interest rates may
be reduced. Actually, the findings in this paper provide further empirical support
to this notion of inflation targeting regimes.
Acknowledgements
We would like to thank Anita AkkaS, Christopher F. Baum, Michael Claxton,
Martin Evans, Richard Froyen and Peter N. Ireland for their invaluable
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MISSING LINK BETWEEN INFLATION UNCERTAINTY AND INTEREST RATES
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suggestions. We are particularly thankful to two anonymous referees for their
helpful comments.
Appendix
Here we report and briefly elaborate the three inflation uncertainty measures.
After 1980, the impulse uncertainty tended to decrease until 1992, after which
there was a big jump in impulse uncertainty. After 1993, the level of impulse
uncertainty increased but the volatility of impulse uncertainty decreased. One
may observe a similar pattern for structural inflation uncertainty. However, after
1997, not only the level but the volatility of the structural uncertainty increased.
The steady-state uncertainty shows a different picture. 1992–97 era had a lower
inflation uncertainty compared with the pre-1992 era and the post-1997 era.
One may look at these uncertainty measures with the help of b coefficients.
Figure 4 plots the estimates of the sum of the autoregressive parts in inflation
specifications. After 1995, the estimated sums of the coefficients were negative.
This could suggest that there is an error correction mechanism in inflation. As
the inflation increases too much, the Bank of England adopts policies to
decrease inflation. However, the inflation figures are quite persistent. After 1974
until 1992, inflation was quite persistent as suggested by the estimated
coefficients of b21b3. These make the structural uncertainty quite low for this
period and put the impulse uncertainty into a decreasing trend.
0.8
0.6
0.4
0.2
− 0.0
− 0.2
− 0.4
− 0.6
1961 1965 1969 1973 1977 1981 1985 1989 1993 1997 2001
Figure 4. Estimate of b21b3.
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References
BALL, L. (1992). Why does high inflation raise inflation uncertainty? Journal of Monetary
Economics, 1, pp. 371–88.
BALL, L. and CECCHETTI, S. (1990). Inflation uncertainty at short and long horizons. Brookings
Papers on Economic Activity, 0, 1, pp. 215–54.
BERNANKE, B. S., LAUBACH, T., MISHKIN, F. S. and POSEN, A. (1999). Inflation Targeting:
Lessons From the International Experience. Princeton, NJ: Princeton University Press.
BERUMENT, H. (1999). The impact of inflation uncertainty on interest rates in the UK. Scottish
Journal of Political Economy, 46, pp. 207–18.
BERUMENT, H. and FROYEN, R. T. (1998). Potential information and target variables for U.K.
monetary policy. Applied Economics, 46, pp. 207–18.
BLANCHARD, O. J. (2003). Fiscal dominance and inflation targeting: lessons from Brazil.
Unpublished Manuscript, MIT Department of Economics.
BLANCHARD, O. J. and FISCHER, S. (1989). Lectures on Macroeconomics. Cambridge, MA:
MIT Press.
BOLLERSLEV, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of
Econometrics, 31, pp. 307–27.
BOMBERGER, T. (1996). Disagreement as a measure of uncertainty. Journal of Money, Credit,
and Banking, 28, 3, pp. 381–92.
CHAN, L. K. C. (1994). Consumption, inflation risk, and real interest rates: an empirical
analysis. Journal of Business, 67, pp. 69–96.
CLARIDA, R., GALI, J. and GERTLER, M. (1999). The science of monetary policy: a new
Keynesian perspective. Journal of Economic Literature, 37, 4, 1661–707.
CUKIERMAN, A. and MELTZER, A. (1986). A theory of ambiguity, credibility, and inflation
under discretion and asymmetric information. Econometrica, 17, pp. 1099–128.
CUKIERMAN, A. and WACHTEL, P. (1979). Differential inflationary expectations and the
variability of the rate of inflation. American Economic Review, 69, 4, pp. 595–609.
DAVIS, G. and KANOGO, B. (1996). On measuring the effect of inflation uncertainty on real
GNP growth. Oxford Economic Paper, 48, pp. 163–75.
ENGLE, R. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance
of United Kingdom inflation. Econometrica, 50, pp. 987–1007.
EVANS, M. (1991). Discovering the link between inflation rates and inflation uncertainty.
Journal of Money, Credit, and Banking, 23, pp. 169–84.
EVANS, M. and WACHTEL, P. (1993). Inflation regimes and the sources of inflation uncertainty.
Journal of Money, Credit, and Banking, 25, pp. 475–511.
FAMA, E. (1975). Short term interest rates as predictor of inflation. American Economic Review,
65, 3, pp. 269–82.
FAMA, E. and GIBBONS, M. (1982). Inflation, real returns and capital investment. Journal of
Monetary Economics, 9, 3, pp. 297–323.
FAMA, E. and SCHWERT, G. (1977). Asset returns and inflation. Journal of Financial Economics,
5, pp. 115–46.
FISCHER, S. (1975). The demand for index bonds. Journal of Political Economy, 83, pp. 509–34.
FRIEDMAN, M. (1977). Nobel lecture: inflation and unemployment. Journal of Political
Economy, 85, pp. 451–72.
FROYEN, R. and WAUD, R. (1987). An examination of aggregate price uncertainty in four
countries and some implications for real output. International Economic Review, 28, 2,
pp. 353–73.
GRIER, K. B. and PERRY, M. J. (1998). On inflation and inflation uncertainty in the G7
countries. Journal of International Money and Finance, 17, pp. 671–89.
GRIER, K. B. and PERRY, M. J. (2000). The effects of real and nominal uncertainty on inflation
and output growth: some GARCH-M evidence. Journal of Applied Econometrics, 15,
pp. 45–58.
HAFER, R. W. (1986). Inflation uncertainty and a test of the Friedman Hypothesis. Journal of
Macroeconomics, 8, 3, pp. 365–72.
HAHN, F. H. (1970). Savings and uncertainty. Review of Economic Studies, 37, pp. 21–4.
HOLLAND, S. (1986). Wage indexation and the effect of inflation uncertainty on employment:
an empirical analysis. American Economic Review, 76, 1, pp. 235–43.
HOLLAND, S. (1988). Indexation and the effect of inflation uncertainty on real GNP. Journal of
Business, 61, 4, pp. 473–84.
r Scottish Economic Society 2005
MISSING LINK BETWEEN INFLATION UNCERTAINTY AND INTEREST RATES
241
HOLLAND, S. (1993). Comment on inflation regimes and the sources of inflation uncertainty.
Journal of Money, Credit and Banking, 27, pp. 514–20.
HOLLAND, S. (1995). Inflation and uncertainty: test for temporal ordering. Journal of Money,
Credit and Banking, 27, pp. 827–37.
JANSEN, D. W. and COSIMONA, T. F. (1988). Estimates of the variance of US. Inflation based
upon the ARCH model: comment (in notes, comments, replies). Journal of Money Credit
and Banking, 20, 3 Part 1, pp. 409–21.
JOHNSON, D. R. (2002). The effect of inflation targeting on the behaviour of expected inflation:
evidence from an 11 country panel. Journal of Monetary Economics, 49, 8, 1521–38.
JUSTER, F. T. and TAYLOR, D. (1975). Towards a theory of saving behavior. American
Economic Review, 65, pp. 203–9.
JUSTER, F. T. and WACHTEL, P. (1972a). Inflation and the consumer. Brookings Papers, 1,
pp. 71–114.
JUSTER, F. T. and WACHTEL, P. (1972b). A note on inflation and the saving rate. Brookings
Papers, 3, pp. 765–78.
KANDEL, S., OFER, A. R. and SARIG, O. (1996). Real interest rates and inflation: an ex-ante
empirical analysis. The Journal of Finance, LI, 1, pp. 205–25.
KONTONIKAS, A. (2004). Inflation and inflation uncertainty in the United Kingdom: evidence
from GARCH modelling. Economic Modelling, 21, pp. 525–43.
MALLIARIS, A. G. and MALLIARIS, M. E. (1991). Inflation rates and inflation: a continuous
time stochastic approach. Economic Letters, 37, pp. 351–6.
MANKIW, N. G., REIS, R. and WOLFERS, J. (2003). Disagreement about inflation expectations.
NBER Working Paper, No. 9796.
MERTON, R. (1975). Theory of finance from the perspective of continuous time. Journal of
Financial and Quantitative Analysis, 10, pp. 659–74.
MISHKIN, F. S. (1981). The real interest rate: an empirical investigation. Carnegie-Rochester
Conference Series on Public Policy, 15, pp. 151–200.
NELSON, E. (2000). UK monetary policy 1972–97: A guide using Taylor rules. Bank of England:
www.bankofengland.co.uk.
Date of receipt of final manuscript: 14 September 2004.
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